What is (-3)/8*ln(-8x+5)+ln(k) ?

The solution to (-3)/8*ln(-8x+5)+ln(k) is ln((k(-8x+5)^{5/8})/(-8x+5))

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simplify (-3)/8*ln(-8x+5)+ln(k)

simplify

\frac{- 3}{8} \cdot ln (- 8 x + 5) + ln (k)

ln (\frac{k ( - 8 x + 5 ) ^{\frac{5}{8}}}{- 8 x + 5})

Solution steps

\frac{- 3}{8} ln (- 8 x + 5) + ln (k)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{- 3}{8} ln (- 8 x + 5) = ln ((- 8 x + 5)^{\frac{- 3}{8}})

= ln ((- 8 x + 5)^{\frac{- 3}{8}}) + ln (k)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln ((- 8 x + 5)^{\frac{- 3}{8}}) + ln (k) = ln (k (- 8 x + 5)^{\frac{- 3}{8}})

= ln (k (- 8 x + 5)^{\frac{- 3}{8}})

Simplify

(- 8 x + 5)^{\frac{- 3}{8}} k : \frac{k ( - 8 x + 5 ) ^{\frac{5}{8}}}{- 8 x + 5}

= ln (\frac{k ( - 8 x + 5 ) ^{\frac{5}{8}}}{- 8 x + 5})

lo g_{e} (a + b) + lo g_{e} (a - b) - 2 lo g_{e} (c)

ln (\frac{( 2 t + 1 ) ^{8}}{( 3 t - 1 ) ^{4}})

ln (\frac{e ^{x} - e ^{- x}}{2})

ln (\frac{114}{132})

ln (\frac{7 x ^{5} - 8}{x ^{2}})

What is (-3)/8*ln(-8x+5)+ln(k) ?
The solution to (-3)/8*ln(-8x+5)+ln(k) is ln((k(-8x+5)^{5/8})/(-8x+5))